11.2: Bar Graphs and Line Graphs

Introduction

All about the Mushers

The students in Mr. Hawkins’ class have continued to learn about the Iditarod. After learning some of the basics about the distances covered, the students began to research information about the teams, where they come from and how many teams have entered the race in the past few years. Mr. Hawkins has asked them to create either a bar graph or a line graph of the data that they discover.

Tommy and Keith decided to investigate where the mushers come from. They did some research on the computer and discovered that in 2010 there were a total of 71 mushers who entered the race. They came from several different states and countries. Tommy and Keith organized their data like this.

46 Mushers from Alaska

13 Mushers from other US states

12 Mushers from other countries

Now they need to put their data into either a bar graph or a line graph.

Yana and Jena have decided to look at how the number of teams has changed over time. They looked at the number of teams that entered the Iditarod in 2006, 2007, 2008, 2009 and 2010. Here is how they organized their data.

2006 – 83 teams

2007 – 82 teams

2008 – 95 teams

2009 – 67 teams

2010 – 71 teams

Now they need to put their data into either a bar graph or a line graph.

Both teams are stuck. They aren’t sure which graph would best show their data. Do you know? If you have a prediction, make a note of it in your notebook. Which graph should the boys use? Which graph should the girls use?

Now pay attention to this lesson and at the end of it, you will be able to determine if you made the correct choice.

You will also be able to see both of the graphs the students made.

What You Will Learn

In this lesson you will learn to demonstrate the following skills:

Make a bar graph to display given data.

Make multiple bar graphs to display and compare given data.

Make a line graph to display given data over time.

Make multiple line graphs to display and compare given data.

Teaching Time

I. Make a Bar Graph to Display Given Data

In the last lesson, you learned to analyze data by determining the mean, median, mode, and range for a set of data values. In this lesson, you will use data to create both bar and line graphs.

Tables and graphs are ways to organize and present information so that it can be easily interpreted by the viewer. Graphs are created to show the relationship between two variables. For example, a graph may be constructed to depict the relationship between an object’s mass and volume or the price of gasoline in relationship to location.

Abar graphis a graph that uses columns to show the comparison of quantities or amounts. For example, the bar graph below depicts the average price of one gallon of gasoline in five states. Looking at the bar graph, you can conclude that Hawaii has the highest average cost per gallon of gasoline and Missouri has the lowest cost.

This bar graph was completed for you to analyze. Next you can learn how to take a set of data and create your own bar graph.

Example

Thirty students in grade seven were asked to state their favorite after school activity. The results of this survey are shown on the table. Create a bar graph to display the information from the data table.

5. Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, since the range in data is not that great, label the vertical axis 0 – 10 by ones.

6. For each activity on the horizontal \begin{align*}(x)\end{align*} axis, draw a vertical column to the appropriate value. For example, you will draw a vertical column to the number “9” for the activity “Watching T.V.”

Example

The data table below depicts the recommended minimum number of hours of sleep people need by age. Create a bar graph using the information from the data table.

Since the graph is about sleep, give the graph the title “Sweet Dreams.”

Label the horizontal axis “Age.”

Label the vertical axis “Hours of Sleep.”

Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0 - 16 by twos.

For each age group on the horizontal \begin{align*}(x)\end{align*} axis, draw a vertical column to the appropriate value. For example, for “Infants,” draw a vertical column to fifteen hours.

Looking at bar graphs can help us to make conclusions about the data.

Looking at the bar graph “Sweet Dreams,” what can you infer about age and the recommended number of hours of sleep?

Looking at the graph, you can see that one needs less sleep as they grow older. It is recommended that infants sleep a minimum of fifteen hours a day. However, it is recommended that adults sleep a minimum of eight hours a day. This difference of seven hours is also known as the range.

Take a few minutes and write down the steps to creating a bar graph.

II. Make Multiple Bar Graphs to Display and Compare Given Data

Amultiple bar graphis similar to a bar graph, but depicts two or three pieces of information for each item on the horizontal \begin{align*}(x)\end{align*} axis, rather than one. For example, a double bar graph may be used to compare the survey answers of males vs. females. A triple bar graph may be used to compare data recorded over a three day period.

Thirty-five girls and thirty-seven boys were asked to state their favorite sport. The results of the survey are displayed on the graph below. You can make several inferences studying the graph “Favorite Sports.” You can see that soccer was the favorite sport among girls and track was the least favorite. More boys preferred basketball than any other choice. Equal numbers of boys and girls stated that their favorite sport was baseball.

Here is a bar graph to show the data.

Example

Frank’s Farm Stand kept track of the number of pounds of vegetables sold over a three-day period. The results are listed on the table below. Create a multiple bar graph to display and compare the amounts of vegetables sold over the three day period.

Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0 - 80 by tens.

For each vegetable on the horizontal \begin{align*}(x)\end{align*} axis, draw a vertical column to the appropriate value three times, one column representing day one, a second column for day two, and a third column for day three.

Choose three colors, one to represent the values for day one, one for the values for day two, and finally one to represent the values for day three.

You can also draw conclusions about data from multiple bar graphs. These comparisons can help you to discover patterns and trends about statistics.

Looking at the bar graph “Frank’s Farm Stand,” what can you infer about the difference in sales over the three day period?

It is apparent that sales of squash, corn, romaine lettuce, and tomatoes increased over the three day period. Zucchini sales dropped on day two, but increased on day three. However, carrot sales declined on day two and again on day three. Note that the same amount of carrots and romaine lettuce were sold on day one.

Example

Taylor created a table to compare the amount of gravitational pull on each planet compared to that on Earth. Create a multiple bar graph to display the information from Taylor’s chart.

Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0-3 by 0.5.

For each planet on the horizontal \begin{align*}(x)\end{align*} axis, draw a vertical column to the appropriate value. For example, the vertical column should reach 0.38 for Mercury to show its gravitational pull.

Next to each vertical column for each planet, draw a vertical column that reaches 1.0 to represent the gravitational pull on Earth.

Choose two colors, one to represent the values for each planet and another to represent the value for Earth.

Looking at the double bar graph “Planet’s Gravitational Pull,” what can you infer about each planet?

This graph compares the gravitational pull on Earth with the other seven major planets. You can see that with the exception of Jupiter and Neptune, all planets have a gravitational pull less than that of Earth. You can see that Mercury and Mars both have a gravitational pull of \begin{align*}0.38 m/s^2\end{align*}. It is apparent that Venus and Saturn are the planets with a gravitational pull that is closest to that of Earth.

Write down the steps to creating multiple bar graphs in your notebook.

III. Make a Line Graph to Display Given Data over Time

Another way to look at data is through a line graph.

Aline graphis a series of connected points that displays data or information that changes over time.

The line graph below illustrates the change in temperature over the first seven days in February in Boston, Massachusetts. Looking at the changes of the line, you can see that the temperature rose the first three days, February \begin{align*}1^{st}\end{align*}, \begin{align*}2^{nd}\end{align*}, and \begin{align*}3^{rd}\end{align*}. On February \begin{align*}4^{th}\end{align*}, the temperature began to decline. The temperature held constant on February \begin{align*}5^{th}\end{align*} and \begin{align*}6^{th}\end{align*}. The temperature began to rise again on February \begin{align*}7^{th}\end{align*}.

Now that you can see how the information is shown in a line graph, the next step is to learn how to make one yourself. Here is an example.

Example

The population for the city of Los Angeles has been recorded on the data table below. Create a line graph to depict the population change from the year 1950 to the year 2000.

Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0 – 4,000,000 by five hundred thousands.

Plot the population for each year on the horizontal axis. For example, put a point at 2,000,000 to show the population for the year 1950. Above the year 1960, put a point at 2,500,000 and so on. Connect the points as you go.

Now that you have created a line graph, you can analyze the data and draw conclusions based on the reported statistics.

Looking at the line graph, what can you infer about the change in population from 1950 to 2000?

It is evident that the population has risen since the year 1950. You can see that the greatest change in population occurred from the years 1950 to 1960 and again from 1980 to 1990. You can see that the smallest change in population occurred between the years of 1990 and 2000. From 1990 to 2000, the population only grew by 200,000 people. Judging by the trend of the graph, you could predict that the population of Los Angeles will continue to increase over time.

Example

The Electronic Energies Alliance recorded the average cost of one gallon of gasoline in the United States for the years 2000-2007. Present the information on the data table on a line graph.

5. Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0 – 3.5 by 0.5.

6. Plot the price of gasoline for each year on the horizontal axis. For example, put a point slightly above 1.5 to show that the cost of one gallon of gas in the year 2000 was $1.59. Place a point slightly above 1 to show that they cost of one gallon of gas in the year 2001 was $1.10. Use a straight edge to connect the points as you go.

Looking at the line graph, what can you conclude about the cost of gasoline from the years 2000-2007?

The price of a gallon of gasoline has increased approximately $1.50 over eight years. You'll notice that the price of a gallon of gasoline dropped in the years 2001 and 2007, but increased in all other years.

IV. Make Multiple Line Graphs to Display and Compare Given Data

Recall that a line graph displays changes in data over time. Amultiple line graphdisplays changes in two or three sets of data over time.

Eleanor Roosevelt School recorded the daily indoor and outdoor temperature for a period of five days. The results of the data collection are presented on the double line graph below. Looking at the graph, you can see that the outdoor temperature was cooler than the indoor temperature. It can also be concluded that as the outdoor temperature decreased, the indoor temperature decreased. The same holds true as the temperature increased.

Now let’s look at some examples of how we can create multiple line graphs and then interpret the data displayed on them.

Example

Full-time and part-time enrollment at California State University for the past five years is recorded on the data table below. Create a multiple line graph to represent the information on the data table.

Look at the range in data and decide how the units on the vertical axis \begin{align*}(y)\end{align*} should be labeled. In this case, label the vertical axis 0 – 14,000 by thousands.

Use one color pen to plot the data for full-time students first. For example, for the year 2003, place a point at 10,000. For the year 2004, place a point between 9,000 and 10,000 to show that the enrollment was 9,500. As you continue to plot the enrollment for each year, use a straight edge to connect the points.

Use another color pen to plot the data for part-time students. For the year 2003, place at point at 2,000. For the year 2004, place a point slightly above 2,000 to show that the enrollment for that year was 2,100. As you continue to plot the enrollment for each year, use a straight edge to connect the points.

Looking at the line graphs, what can you conclude about enrollment at California State University?

You can see that the number of full-time students enrolled increased by 3,300 students from 2003 to 2007. While full-time enrollment declined between 2003 an 2004, it increased every other year. The number of part-time students enrolled increased by 550 students from 2003 to 2007. It is apparent that the increase in full-time enrollment was greater than the increase in part-time enrollment.

Real Life Example Completed

All about the Mushers

Here is the original problem once again. Reread it and then look at the graphs created.

The students in Mr. Hawkins’ class have continued to learn about the Iditarod. After learning some of the basics about the distances covered, the students began to research information about the teams, where they come from and how many teams have entered the race in the past few years. Mr. Hawkins has asked them to create either a bar graph or a line graph of the data that they discover.

Tommy and Keith decided to investigate where the mushers come from. They did some research on the computer and discovered that in 2010, there were a total of 71 mushers who entered the race. They came from several different states and countries. Tommy and Keith organized their data like this.

46 Mushers from Alaska

13 Mushers from other US states

12 Mushers from other countries

Now they need to put their data into either a bar graph or a line graph.

Yana and Jena have decided to look at how the number of teams has changed over time. They looked at the number of teams that entered the Iditarod in 2006, 2007, 2008, 2009 and 2010. Here is how they organized their data.

2006 – 83 teams

2007 – 82 teams

2008 – 95 teams

2009 – 67 teams

2010 – 71 teams

Now they need to put their data into either a bar graph or a line graph.

Let’s start with the boys. They are looking at the number of mushers from different places. Nothing is changing in their data over time-therefore it makes the most sense for them to use a bar graph. They are also looking at the frequency of mushers from each location. Here is a bar graph that best shows their data.

Next, we can look at the girls. The girls are looking at how the number of teams that has entered the Iditarod has changed over time. They are comparing data that has changed. When we compare data and how it changes, we use a line graph. That is the best way to show this data.

Vocabulary

Bar Graph

a graph designed to compare data and show the frequency of the data.

Multiple Bar Graph

a graph that shows how different strands of data compare over time. It shows the frequency of this data and compares it at the same time.

Line Graph

shows how data changes over time.

Multiple Line Graphs

show how different strands of data change over time.

Technology Integration

Time to Practice

Directions: The multiple bar graph below depicts the number of Major League Baseball teams in each state, as well as the number of World Series Championships won by each state. Use the graph to answer the questions.

1. How many Major League Baseball teams are represented on the graph? _____

2. How many World Championships are represented on the graph? _____

3. How many of states on the graph have won a Major League Championship? _____

4. Which states have equal numbers of Major League Baseball teams? _____

5. Which state has won the greatest number of World Championships? _____

Directions: Twenty students in \begin{align*}6^{th}\end{align*}, \begin{align*}7^{th}\end{align*}, and \begin{align*}8^{th}\end{align*} grade were asked to state how many of each of the following electronic devices their homes contained.

6. Create a multiple bar graph to display the information from the table.

Name of Device:

\begin{align*}6^{th}\end{align*}Grade Answers:

\begin{align*}7^{th}\end{align*}Grade Answers:

\begin{align*}8^{th}\end{align*}Grade Answers:

Television

35

28

31

DVD Player

30

28

20

Computer

19

20

17

Game System

15

14

20

Video Camera

14

17

12

7. What is the most common electronic device in the sixth grade?

8. What is the most common electronic device in the seventh grade?

9. What is the most common electronic device in the eighth grade?

10. What is the least common electronic device in the sixth grade?

11. What is the least common electronic device in the seventh grade?

12. What is the least common electronic device in the eighth grade?

Directions: The table below shows the number of tickets sold at the Phoenix Zoo and the Seattle Zoo since 1998.

13. Create a multiple line graph using the data from the table.

Year:

Number of Tickets Sold at Phoenix Zoo:

Number of Tickets Sold at Seattle Zoo:

1998

547,000

601,000

1999

562,000

602,500

2000

569,000

603,700

2001

566,000

605,000

2002

569,000

604,000

2003

572,000

605,100

2004

576,000

606,000

2005

575,500

605,800

2006

579,000

607,000

2007

580,000

608,000

14. Which zoo sold more tickets in 2003?

15. Which zoo sold more tickets in 2005?

16. Which was the best year for sales at the Phoenix zoo?

17. Which was the best year for sales at the Seattle zoo?

18. Based on this information, can we say which zoo is more popular? Why?

19. Based on this data, will sales increase or decrease in 2008 at the Phoenix zoo?

20. Based on this data, will sales increase or decrease in 2008 at the Seattle zoo?

Directions: The data table below depicts the increase in cost of a movie ticket each year since 2000.

Year:

Price of a Ticket:

2000

$5.50

2001

$5.75

2002

$6.00

2003

$6.25

2004

$6.50

2005

$7.25

2006

$8.00

2007

$9.25

21. Decide which type of graph, bar or line, should be used to represent the information in the data table.

22. Use the information on the data table to create the graph you’ve chosen.

Directions: The data table below depicts the number of newspapers in circulation (in millions) over a period of three days.

23. Decide which type of graph, bar or line, should be used to represent the information in the data table.

24. Use the information on the data table to create the graph you’ve chosen.